¹ For a critical review of work in “general systems theory,” see Handy, Rolo and Kurtz, Paul, “A Current Appraisal of the Behavioral Sciences,” American Behavioral Scientist, 7 (03, 1964, supplement), 137–141Google Scholar.

² The most complete treatment of the question of causation in international relations can be found in Waltz, Kenneth N., Man, the State and War: A Theoretical Analysis (New York: Columbia University Press, 1959)Google Scholar. See also Goodman, Jay S., “The Concept of ‘System’ in International Relations Theory,” Background, 8 (02 1965), 257–268CrossRefGoogle Scholar.

³ “Though the systemic model does not necessarily preclude comparison and contrast among the national subsystems, it usually eventuates in rather gross comparisons based on relatively crude dimensions and characteristics”: Singer, J. David, “The Level-of-Analysis Problem in International Relations,” World Politics, 14 (10 1961), p. 83Google Scholar. The subsystemic model, though also comparative, “permits significant differentiation among our actors in the international system”: ibid., p. 82.

⁴ Recent substantial contributions to the compilation and analysis of aggregate cross-national data include Banks, Arthur S. and Textor, Robert B., A Cross-Polity Survey (Cambridge, Mass.: M.I.T. Press, 1963)Google Scholar; Russett, Bruce M.et al., World Handbook of Political and Social Indicators (New Haven, Conn.: Yale University Press, 1964)Google Scholar; and Merritt, Richard L. and Rokkan, Stein (eds.), Comparing Nations: The Use of Quantitative Data in Cross-National Research (New Haven, Conn.: Yale University Press, 1966)Google Scholar. Cross-national comparisons of data presented later in this article are given in Chadwick F. Alger and Steven J. Brams, “Patterns of Representation in National Capitals and Intergovernmental Organizations,” World Politics forthcoming.

⁵ Haas, Ernst B., Beyond the Nation-State: Functionalism and International Organization (Stanford, Calif.: Stanford University Press, 1964), p. 53Google Scholar, italics in original.

⁶ Diplomatic exchanges refer to the number of career-level diplomats each country received from all other countries in 1963–64, as reported in lists of diplomats in 104 national capitals published by the host countries. Trade data are for 112 countries in 1962 and were taken from the International Monetary Fund and International Bank for Reconstruction and Development, Direction of Trade, Annual 1958–62 (Washington, D. C., 1964)Google Scholar. The number of memberships in 161 IGO's which each country shared in 1963 with every one of 117 other countries was computer-calculated from the country-IGO table given in the Worldmark Encyclopedia of Nations: United Nations (New York: Worldmark Press, 1963), pp. 258–265Google Scholar.

⁷ The effect appears to be greatest when information from the environment is rich and differentiated. See Verba, Sidney, “Assumptions of Rationality and Non-Rationality in Models of the International System,” World Politics, 14 (10 1961), p. 100CrossRefGoogle Scholar.

⁸ For a discussion of the political significance of each of these transaction flows, see Brams, Steven J., Flow and Form in the International System (unpublished doctoral dissertation, Northwestern University, 1966), pp. 29–37Google Scholar.

⁹ For limited empirical evidence of this correspondence, see ibid., pp. 70–71.

¹⁰ Actually, the model predicts that A will send slightly more than one percent of its corps to B, since A is not allowed by the model to send diplomats to itself. Those diplomats which this “no self-exchange” restriction disallows are, in effect, spread around to other countries.

¹¹ Predictions might also be based on the population or national income of a country. Such a procedure is suggested by Georgio Mortara for measuring the relative intensity of trade flows. See his “Indices of the Intensity of Trade between Two Countries,” PROD Translations [American Behavioral Scientist], 3 (02 1960), 14–20Google Scholar. For a “polarization” index of trade flows, see Smoker, Paul, “Trade, Defence and the Richardson Theory of Arms Races: A Seven Nation Study,” Journal of Peace Research, 2 (1965), 161–176CrossRefGoogle Scholar.

¹² Savage, I. Richard and Deutsch, Karl W., “A Statistical Model of the Gross Analysis of Transaction Flows,” Econometrica, 28 (07 1960), 551–572CrossRefGoogle Scholar. For a computer program of this model, see Alker, Hayward R. Jr., Behavioral Science, 7 (10 1962), 498–499Google Scholar.

¹³ Alger and Brams, op. cit.

¹⁴ If the predictions for the non-existent exchanges in the Savage-Deutsch model did not affect the other predictions, they could simply be ignored. Since there are a fixed number of diplomats to be distributed in the system, however, allocations made by the Savage-Deutsch model to predictions for the non-existent exchanges lower the values of the predictions for the actual exchanges. The Goodman model, by disallowing non-existent exchanges as well as self-exchanges, distributes all diplomats in the system to fewer pairs of countries (only those that exchange diplomats with each other) and thereby raises the values of the predictions for the exchanges that actually occur.

¹⁵ Goodman, Leo A., “Statistical Methods for the Preliminary Analysis of Transaction Flows,” Econometrica, 31 (01–April 1963), 197–208CrossRefGoogle Scholar; and “A Short Computer Program for the Analysis of Transaction Flows,” Behavioral Science, 9 (04 1964), 176–186CrossRefGoogle Scholar. The mathematical model for a computer program, but not an actual computer program, is given in the latter article; for a program of the model written for the CDC 3400 computer, see my “A Generalized Computer Program for the Analysis of Transaction Flows,” Behavioral Science, 10 (10 1965), 487–488Google Scholar. A write-up and listing of this program are available from the Vogelback Computing Center, Northwestern University.

¹⁶ On this point, see Deutsch, Karl W. and Isard, Walter, “A Note on a Generalized Concept of Effective Distance,” Behavioral Science, 6 (10 1961), 308–311CrossRefGoogle Scholar. Criteria for measuring the political distance between countries are suggested by Wright, Quincy in A Study of War (Chicago: University of Chicago Press, 1942), II, pp. 1250–1252Google Scholar. See ibid., pp. 1466–1471, for actual judgments which Wright made of the political and other “distances” separating the seven great powers prior to World War II.

¹⁷ For evidence on this point, see Fox, Annette B., The Power of Small States: Diplomacy in World War II (Chicago: University of Chicago Press, 1959)Google Scholar.

¹⁸ Although the salience criteria we have used are symmetrical—that is, they apply to flows in both directions for each pair of countries—I have elsewhere suggested an index to measure the asymmetry, or imbalance, of transaction flows between two countries. See my “A Generalized Computer Program for the Analysis of Transaction Flows,” op. cit., p. 488.

¹⁹ That is, the total number of IGO affiliations two nations have in common must exceed the predicted number by either one or two memberships.

²⁰ Although Savage and Deutsch suggest statistical procedures for determining significant RA's, these involve assuming a common consignment size for the flows between all pairs of countries which seems a no less arbitrary procedure than that used here to determine salience. See Savage and Deutsch, op. cit., pp. 567–571.

²¹ Ibid., passim.

²² Goodman, Leo A., “On the Statistical Analysis of Mobility Tables,” American Journal of Sociology, 70 (03 1965), p. 578CrossRefGoogle Scholar.

²³ Ibid., p. 573. Although not computed here, this statistic can also be calculated for individual countries. See Brams, “A Generalized Computer Program for the Analysis of Transaction Flows,” loc. cit.

²⁴ See Hays, William L., Statistics for Psychologists (New York: Holt, Rinehart and Winston, 1963), p. 613Google Scholar.

²⁵ Besides the cleavages that exist between nations, the viability of “linkage groups” connecting a nation's domestic community with the international environment must also be taken into account in evaluating the permeability of national boundaries. See Deutsch, Karl W., “External Influences on the Internal Behavior of States,” in Farrell, R. Barry (ed.), Approaches to Comparative and International Politics (Evanston, Ill.: Northwestern University Press, 1966), pp. 5–26Google Scholar.

²⁶ It is interesting to note that the search by theorists for a structural order in international relations has a parallel in the history of modern art, where the desire to render an objective representation of reality (in contrast to the subjectivism of impressionistic painting) first took shape in the work of the great French painter, Paul Cézanne. See Read, Herbert, A Concise History of Modern Painting (New York: Frederick A. Praeger, 1959), pp. 13–21Google Scholar.

²⁷ Deutsch and Singer have shown that a nation's allocation of unequal amounts of attention to other nations may critically affect the likelihood of its initiating international conflict. See Deutsch, Karl W. and Singer, J. David, “Multipolar Power Systems and International Stability,” World Politics, 16 (04 1964), 390–406CrossRefGoogle Scholar.

²⁸ Problems of “disorganized complexity,” characteristic of the physical sciences, are amenable to this approach, but the problems of “organized complexity” that are characteristic of the social sciences are generally not soluble in this way. See Weaver, Warren, “A Quarter Century in the Natural Sciences,” Annual Report of the Rockefeller Foundation, 1958 (New York: Rockefeller Foundation, 1959), pp. 7–15Google Scholar; and Kemeny, John G., A Philosopher Looks at Science (Princeton, N.J.: D. Van Nostrand Company, Inc., 1959), p. 249Google Scholar.

²⁹ The interactions of people and the analogous problem of schematically summarizing the group structures which they form is treated in sociometry. For a review of various approaches, see Coleman, James S., Introduction to Mathematical Sociology (New York: Free Press of Glencoe, 1964), pp. 14–16, 430–468Google Scholar; and Nosanohuk, Terrance A., “A Comparison of Several Sociometric Partitioning Techniques,” Sociometry, 26 (03 1963), 112–125CrossRefGoogle Scholar. Factor analysis has been used in recent studies by political scientists to group together nations that behave in similar ways across a set of variables. Applied to the D or RA transaction-flow matrices in this study, however, factor analysis would not necessarily produce groups of nations that have a high density of internal linkages, since nations would be grouped together on the basis of the similarity of their patterns of transaction flows with nations not necessarily in their factor groups—not according to whether the nations in each group had high flows with each other. See Russett, Bruce M., “Delineating International Regions,” in Singer, J. David (ed.), Quantitative International Politics: Insights and Evidence (New York: Free Press of Glencoe, forthcoming)Google Scholar; Russett, Bruce M., “Discovering Voting Groups in the United Nations,” this Review, 60 (06 1966), 327–339Google Scholar; and Banks, Arthur S. and Gregg, Philip M., “Grouping Political Systems: Q-Factor Analysis of A Cross-Polity Survey,” American Behavioral Scientist, 9 (11 1965), 3–6CrossRefGoogle Scholar.

³⁰ Alexander, Christopher and Manheim, Marvin L., HIDECS 2: A Computer Program for the Hierarchical Decomposition of a Set with an Associated Linear Graph (Cambridge, Mass.: Civil Engineering Systems Laboratory, M.I.T., 1962)Google Scholar. The mathematical model on which HIDECS 2 is based is given in Alexander, Christopher, Notes on the Synthesis of Form (Cambridge, Mass.: Harvard University Press, 1964), pp 174–191Google Scholar. This model serves as the basis for a fascinating theory of design presented in ibid.

³¹ The importance of maps to the study of international politics has long been recognized. While cognizant of their misuses in the past, Harold and Marqaret Sprout assert that “one can scarcely hope to understand the foreign policies and interactions of states without the aid of maps …”: “Geography and International Politics in an Era of Revolutionary Change,” in Jackson, W. A. Douglas (ed.), Politics and Geographic Relationships (Englewood Cliffs, N. J.: Prentice-Hall, 1964), p. 38Google Scholar. On the value of graphical methods of data reduction, see Tukey's, John W. “Statistical and Quantitative Methodology,” in Ray, Donald P. (ed.), Trends in Social Science (New York: Philosophical Library, 1961), pp. 121–122, 128Google Scholar; and his “The Future of Data Analysis,” Annals of Mathematical Statistics, 33 (03 1962), pp. 60–61Google Scholar.

³² On the concept of “critical boundary,” see Boulding, Kenneth E., Conflict and Defense: A General Theory (New York: Harper & Brothers, 1962), pp. 265–266Google Scholar; and Scott, Andrew M., “Internal Violence as an Instrument of Cold Warfare,” in Rosenau, James N. (ed.), International Aspects of Civil Strife (Princeton, N. J.: Princeton University Press, 1964), p. 160Google Scholar.

³³ See Simon, Herbert A., “The Architecture of Complexity,” Proceedings of the American Philosophical Society, 106 (12 12, 1962), 467–482Google Scholar. For a very persuasive argument that this i not true of “natural” cities, see Alexander, Christopher, “A City Is Not a Tree,” Architectural Forum, 122 (2 pts.; 04, 05 1965), 58–62, 58–61Google Scholar.

³⁴ BLDUP and all but one of the other decomposition programs employed in the subsequent analysis are described in Alexander, Christopher, HIDECS 3: Four Computer Programs for the Hierarchical Decomposition of Systems Which Have an Associated Linear Graph (Cambridge, Mass.: Civil Engineering Systems Laboratory, M.I.T., 1963)Google Scholar. For a description of HYPAP, not given in HIDECS 3 see Moore, Gary T., “Computer Program—The Hierarchical Decomposition of a System with an Associated Linear Graph” (Department of Architecture, University of California, Berkeley, 01 1965, ditto)Google ScholarPubMed.

³⁵ In the simplest representation of such overlap, nations A and B are triangle-connected if their flows are related thus:

they are tetrahedron-connected if their flows are related not only through C and D but also through a third nation (not pictured here), E. All of the EQCLA subgroups in Figure 7 are triangle-connected, but none meet the more stringent criterion of tetrahedron-connectedness.

³⁶ Only 28 of the 51 nations with coincidentally salient linkages at the first level met the threshold criteria at the second level.

³⁷ For an example of a longitudinal analysis of flows using the techniques set forth in this article, see my “Trade in the North Atlantic Area: An Approach to the Analysis of Transformations in a System” (paper delivered at the Third European Peace Research Conference, Peace Research Society (International), Vienna, Austria, 09 2–4, 1966)Google Scholar.